Need cardio, weights advice

I need to go to the gym on a regualr basis, especially now I wont be cycling to school 3 times a week 35/40mins there and 35/40 mins back.

So if I go to a salsa class on sundays and a yoga class on mondays.
4 days a week lift weights for 15mins then jog/run mix on threadmil for 15 mins and either a arm cycle thing, rowing machine etc for 15 mins.

Is this generally okay, or is there anything that needs changing?

I know it wholely depends on each individual persons body, but should there typically be a defference after one month?
I really have a personal deadline/goal of around 2-1/2 to 3months.

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End of August goal!

Main goal

Height 4'10''

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